*THE POPULAR SCIENCE MONTHLY.*

these difficult ones. Not many of these occur; the author, however, has a purpose in these few. For the most part the pupil is able by the grading to go on without questioning, as will readily be seen by examining the problem of which Fig. 4 is the solution, and the questions based upon it:

"Place three circles so that the circumference of each may rest upon the centers of the other two, and find the center of the curvilinear figure which is common to all the three circles."

"That point in an equilateral triangle which is equally distant from each side of the triangle, and equally distant from each of the angular points of the triangle, is called the center of the triangle."

"Can you make an equilateral triangle whose sides shall be two inches, and find the center of it?"

"Can you place a circle in an equilateral triangle?"

"Can you divide an equilateral triangle into six parts that shall be equal and similar?"

"Can you divide an equilateral triangle into three equal and similar parts?"

To exercise to the utmost the pupil's power to invent, problems are given with certain restrictions: "Can you divide an angle